As a game system that controls the progression of a game according to elements that are selected from a plurality of selective elements, a bingo game machine is per se known (for example, Patent Literature #1) that establishes correspondence between a plurality of numbers that are the subjects to be selected by a lottery device which serves as an element selection device, and a plurality of numbers that are respectively allocated to each of a plurality of cells which serve as game elements, that makes the cells corresponding to the numbers which are selected activate in series, and that gives a reward to a user when the activated cells form some particular fixed arrangement.